Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on pseudocompact spaces and $ k\sb{R}$-spaces


Author: Akio Kato
Journal: Proc. Amer. Math. Soc. 63 (1977), 175-176
MSC: Primary 54D30; Secondary 54G20
MathSciNet review: 0433384
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Utilizing the Stone-Čech compactification of an uncountable discrete space, we construct a pseudocompact space X which belongs to Frolík's class $ {\mathfrak{P}^ \ast }$ but $ {k_R}X$ is not pseudocompact.


References [Enhancements On Off] (What's this?)

  • [1] J. L. Blasco, An example of a space X in $ {\mathfrak{P}^ \ast }$ for which $ {k_R}X$ is not pseudocompact, Collect. Math. (to appear).
  • [2] Z. Frolík, The topological product of countably compact spaces, Czechoslovak. Math. J. 10 (85) (1960), 339-349. MR 22 #8480 MR 0116304 (22:7099)
  • [3] N. Noble, Countably compact and pseudocompact products, Czechoslovak. Math. J. 19 (94) (1969), 390-397. MR 40 # 1968. MR 0248717 (40:1968)
  • [4] -, The continuity of functions on cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198. MR 41 #2636. MR 0257987 (41:2636)
  • [5] R. C. Walker, The Stone-Čech compactification, Ergebnisse Math. Grenzgebiete, Bd. 83, Springer-Verlag, Berlin and New York, 1974. MR 52 #1595. MR 0380698 (52:1595)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D30, 54G20

Retrieve articles in all journals with MSC: 54D30, 54G20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0433384-6
PII: S 0002-9939(1977)0433384-6
Keywords: Pseudocompact, $ {k_R}$-space, Stone-Čech compactification
Article copyright: © Copyright 1977 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia